Given the functions f(x)= 1/x−4 +3 and g(x)=1/x+1 +6 .Which statement describes the transformation of the graph of function f onto the graph of function g?The graph shifts 5 units right and 3 units down.The graph shifts 3 units left and 5 units up.The graph shifts 5 units left and 3 units up.The graph shifts 3 units right and 5 units down.
Accepted Solution
A:
ANSWERThe graph shifts 5 units left and 3 units up.EXPLANATIONThe given functions are:[tex]f(x) = \frac{1}{x - 4} + 3[/tex]and[tex]g(x) = \frac{1}{x + 1} + 6[/tex]We want to transform f(x) so that, it coincide with the g(x).The required transformation is [tex]f(x+5)+3[/tex]Let us see why this works.[tex]f(x+5)+3 = \frac{1}{x + 5- 4} + 3 + 3[/tex][tex]f(x+5)+3 = \frac{1}{x + 1} + 6 = g(x)[/tex]The transformation f(x+5)+3 will shift f(x) 5 units left and 3 units up.The third choice is correct.